Lines Based Construction

What is the angle between two parallel line?

Draw a line $l$. Draw a perpendicular to $l$ at any point on $l$. On this perpendicular choose a point $X, 4 \mathrm{cm}$ away from $l$. Through $X$, draw a line m parallel to $l$.

In the given figure, $l\parallel m$. Find the value of $b-a$.

In the figure if $l\parallel m$ and $\angle 1=2x+y$,$\angle 4=x+2y$ and $\angle 6=3y+{20}^0$. Find $\angle 7$ and $\angle 8$.

In the following fig, FD and AE are parallel to each other and $\angle ABC={49}^0$, then $\angle ABC+\angle DCB$ is equal to

A parking lot for a city mall is shows below. The painted lines that separate the parking spaces are parallel.

Parking space number $378$ is inclined at $60°$ to the horizontal line. At what angle is parking space $380$ inclined to the horizontal line? Why?

In the given figure, $l\parallel m\parallel n$ and $\angle 1= 60°$. Find $\angle 2$.

What is corresponding angles?

If the lines $l$ and $m$ parallel, then find $x$ and all other angles in the figure given.

Draw two parallel lines on either side of a given line, one at a distance of $2.5$cm and the other at a distance of $3$ cm.

In the below given figures $\left(i\right)\text{ and} \left(ii\right)$, find the value of $x$ if $l \parallel m$.

figure$\left(i\right)$ and figure $\left(ii\right)$ 

Describe two ways to prove $\angle 1=\angle 4$.

Karthik wrote the following steps to construct a line parallel to the given line. His steps are given below.

$\left(1\right)$ Draw line $l$ and mark a point, $M$ on the line. Mark another point, $N$ above the line and join $MN$.

$\left(2\right)$ With $M$ as the centre, draw an arc of convenient radius cutting $l$ at $O$ and $MN$ at $P$.

$\left(3\right)$ With $N$ as the centre and the same radius as before, draw an arc, cutting $MN$ at $Q$.

$\left(4\right)$ With $Q$ as the centre and the radius as before, cut an arc on the previously drawn arc at $R$. 

$\left(5\right)$ Join $RN$

Did Karthik write the steps correctly? If not, which is the first step he made the error?

Manju drew a line $l$ and followed all steps to construct a line parallel to it through $D$. However, she made a mistake during the construction. The figure she constructed is given below.

Her friend checked the work made the statement: "With radius equal to $BC$ and $G$ as the centre the cut an arc on $GF$. Then join point D and the point of intersection of $GF$ with the arc, to get the line parallel to $l$"

Her friend mentioned the reason: "To make lines parallel, the alternate interior angles must be made equal"

What can we say about the statement and the reason?

In the adjoining figure, $l\parallel BC$ and $AB \mathrm{and} AC$ are the trasversals. If $\angle 2=\angle 3$ and $\angle 1=\frac{1}{4}\angle 2$, then the measure of $\angle B$ is 

In the given figure, $PQ=PR$, $RQ=RS$, $ST\parallel QR$. Find the measures of $\angle RST$ and $\angle TRS$.

$ABCD$ is a parallelogram, $\angle ADB=52°, \angle CDB=30°, BC=6.3 \mathrm{cm}$ and $DC=10 \mathrm{cm}$. Find $\angle ABD$ and $\angle DBC$.

In the figure given, $BD\parallel AE$. If $\overline{CE}=3 \mathrm{cm}$, what is the length of $\overline{AC}$?

In the given figure. $AB\parallel CD$ and $BC\parallel DE$. Show that $\angle x=\angle y$.

If $AB\parallel CD\parallel MN$, reflex angle $\angle BOM=310°$ and $\angle OMN=20°$, find the value of $\angle OBA$